10am ET/3pm BST: This morning we're tracking the major rearrangements of European politics and how they might register across the globe – welcome to our live blog coverage. Tom McCarthy here in New York, and here's a summary of the latest developments:

•France struck out in a major new direction on Sunday, ejecting Nicolas Sarkozy from the presidency and voting in Socialist party candidate François Hollande. Hollande campaigned on a platform of promoting growth as opposed to the mere elimination of debt. He campaigned against unpopular austerity measures.

•In Greek parliamentary elections voters rejected two mainstream parties who had helped negotiate austerity plans meant to pull the country out of its debt crisis in favor of extreme candidates who echoed the popular outcry against austerity. The move cast further doubt on Greece's long-term ability to stay in the eurozone.

•American markets reacted with indifference at the start of trading Monday, with the Dow Jones average down 0.2%. Built-in expectations of a swing away from austerity in Europe coupled with diminishing fears of a sharp new European downturn contributed to market stability.

•Hollande's election was seen as threatening to the Franco-German co-operation on corralling European debt through tighter budgetary discipline. German chancellor Angela Merkel sought to tamp down speculation of a fracturing of European leadership. "I may say from my side that François Hollande will be welcomed with open arms here in Germany by me," Merkel said Monday. "We will work together well and intensively."

• The euro was trading at its lowest level in months after the developments of the weekend. Markets in Europe and Asia slumped with the news.

10.45am ET/3.45pm BST: What do the developments in Europe mean for the United States? My colleague Dominic Rushe is watching the first reactions of American markets and provides a little historical context:

David Howells/guardian.co.uk

The US stock markets are still nonplussed by the European news. Last year the Greek debt crisis helped wipe out a spring rally in the US stock markets and investors here seemed terrified that Europe was made up of country-sized Lehman Brothers all waiting to fall like dominoes.

Jacob Kirkegaard at the Peterson Institute wrote a great piece last week that may explain the as-yet muted reaction to the death of "Merkozy" and the electoral mess in Greece. His basic argument is that very little has really changed after the election of Hollande and that the Greeks face a dilemma that hasn't changed: agree to reform and stay in Europe or leave. And they don't want to leave.

We caught up with Kirkegaard this morning. He said that Hollande had little real room for manoeuvre and that Greece still faced the same choice: "Do you want to stay in Europe or join the Levant?"

He's betting they want to stay.

10.54am ET / 3.54pm BST: Does the potential collapse of the eurozone mean American investments are vulnerable this morning in a new way?

There's one US investor who doesn't appear to be worried: Warren Buffett.

Berkshire Hathaway Chairman Warren Buffett is surrounded by the press at the company trade show in Omaha, Nebraska. Photograph: Rick Wilking/Reuters

Speaking this morning to CNBC, the billionaire head of Berkshire-Hathaway said he expects Europe to steer its way out of its debt crisis, but not without some pain.

The U.S. economy, in any case, is on a "different path" from Europe, with the US having already addressed insolvency in its biggest banks, Buffett told CNBC's Becky Quick.

Buffett also spoke to the difficulty of acting in 17 countries simultaneously in Europe. The US government can – and did – come to the rescue of the big banks with little discussion outside a tight group of officials acting at the behest of a sole chief executive. Not so in Europe.

11.15am ET/4.15pm BST: Which development will have more long-term consequences for Europe: the election of François Hollande or Greece's move for the exits of the eurozone?

Matthew Yglesias says despite his campaign rhetoric, Hollande may find that his hands are tied if he seeks a major shift in European fiscal policy:

All that said, when very plausible story of what happens next is simply that the European Central Bank will decide it needs to bring the continent's newest leader to heel. If the ECB signals that it will only support the French banking system and the French economy if Hollande sticks with the status quo program, then Hollande may well have no choice. Elections in Europe aren't necessarily what they used to be. Nobody's crying over Silvio Berlusconi but he was Italy's elected Prime Minister and he lost power not in an election but it a made-in-Frankfurt call by the central bank.

Backing up a minute: I don't think you want to read European elections in terms of any particular ideological tide. This is very much a Larry Bartels world in which voters toss out incumbents and reward insurgents if the economy is bad, never mind the specifics of their platforms. Hollande's victory in France is no more a harbinger of a general leftward shift than Rajoy's victory in Spain a little while ago heralded a general rightward shift; these are just the "outs" benefiting from the fact that they aren't in, and the economy stinks.

The fragmentation in Greece will inevitably raise the question of whether the country will leave, or be pushed out of, the euro zone. Until now European officials have been adamant that any breach of Greece's second austerity and reform plan would lead to the halting of its rescue funds.

11.24am ET/4.24pm BST:Euro up, Greece down: it might be a summary of what will happen in the next year. In any case it's what happened at the close of the trading day in Europe Monday.

Greek stocks were down 6.7 percent, on the sense that a series of carefully crafted austerity plans to deliver the country from its debt crisis were on the verge of being summarily jettisoned.

The euro, meanwhile, reversed its sharp dive to maintain parity with the dollar, the AP reports:

In the currency markets, the euro recovered its poise after falling to a three-month low against the dollar during Asian trading hours. It was up 0.5 percent at $1.3040, having earlier fallen to $1.2972.

Earlier in Asia, Japan's Nikkei 225 index plunged 2.8 percent to close at 9,119.14 — its lowest finish in three months — with the market's export sector also sapped by a rising yen. Hong Kong's Hang Seng slid 2.6 percent to 20,536.59. In other Asia markets, Australia's S&P/ASX 200 lost 2.2 percent to 4,301.30 and South Korea's Kospi shed 1.6 percent to 1,956.44.

11.40am ET/4.40pm BST: In the heady early-'90s days of Maastricht and eurozone cheerleading, a vocal minority warned that economies so vastly different could never be made to stick together in the long term.

It is premature to take up the original euro criticism as having been correct. But Derek Thompson of the Atlantic is onto a chart that illustrates, somewhat mirthfully, its truth.

The chart, by JP Morgan analyst Michael Cembalest, measures "dispersion" among economies of the euro-zone and in other monetary unions such as Gulf State GCC countries. The taller the bar, the greater the dissimilarity in member economies.

The eurozone: slightly less aligned than a random collection of countries beginning with the letter "M." Public Domain

First, economic non-performance by an incumbent government is not acceptable. Excuses wear thin with anxious voters.

Second, a failure to deal with fiscal problems early on results in economic and political crisis down the road, when the cure becomes much more extreme.

And finally, so long as governments impose anti-growth, high tax policies that impede economic vitality, incumbent governments will fail both to meet their debt obligations and satisfy popular demands for jobs and prosperity.

Not everyone agrees that the lessons of the European elections are so obvious:

Pretending to draw lessons about America from an election in France is political amateur hour

12.05pm ET/5.05pm BST: How is austerity where you live? Do you need more austerity, or less? Who has the right to impose austerity?

My colleague Katie Rogers has a short history of how a single word came to summarize the debate over Europe's future.

"Austerity" achieved the questionable honor of being Merriam-Webster's Top Word of 2010 -- runners up included "moratorium" and "socialism."

"Austerity no longer needs to be our fate," Hollande said in his victory speech Sunday evening.

The two main political parties in Greece are under fire, but their rejection is as much an attack on externally imposed "austerity" rules as the political status quo.

"We are talking about a complete collapse of the party system as we have known it, which opens up new concerns about Greece's ability to govern itself," Dimitris Keridis, professor of political science at Athens' Panteion University, told The Guardian's Helena Smith Sunday.

In France, eyes are locked on Germany -- specifically, Merkel's reaction to Hollande's promise to end "austerity."

"Perhaps the reality of the euro zone right now is that this isn't just about what Hollande does now," writes The Washington Post's Ezra Klein. "It's about what Merkel wants to do now, and what the [European Central Bank] wants to do now."

12.22pm ET/5.22pm BST: President Obama's former chief of staff, Rahm Emanuel, now mayor of Chicago, doesn't think François Hollande is presidential material, thank you very much.

"To me, [Hollande] has more of the head of a prime minister than of a president," Emanuel told a group at the French ambassador's residence, according to a Libération report (quotation translated back into English from the French). Emanuel added that in his professional opinion Hollande isn't going to be able to grow into the job, either.

Libération also wades into one of the loonier aspects of the French election as interpreted by Americans. The paper quotes a Washington diplomat as saying that the new French president better get somebody over here pronto to explain to the American market that even though Hollande is a member of the Socialist Party, he's not actually a socialist, or at least not like that.

"What I'd suggest to Francois Hollande is to send very quickly a representative to New York, to reassure the markets which are very nervous," the paper quotes an anonymous official as saying. "The word 'socialist' still makes investors here afraid."

We're certain that President Obama – socialist-in-chief to some of his sharper critics – would love to appear with Hollande on a multi-state barnstorming tour to open a discussion with Americans about what socialism is and how neither man embodies it.

12.55pm ET/5.55pm BST: And now, From the Comments, a call for a deeper take on the parliamentary elections in Greece:

So far we've had the French elections in great detail - locally, nationally, internationally, as it happens. Whereas the quite extraordinary results from the elections in Greece have mostly been reported from a business and economics perspective. Could we have a bit more of what's going on there socially and politically please? It seems pretty significant.

First, back to the results in Greece. Greek voters rejected the middle and went to the ends. The voters approved politicians on the far right and left who virulently opposed the deficit-reduction policies demanded by international creditors.

The conservative New Democracy party came in first but with 18.9% of the vote. The far right Chrysi Avgi (Golden Dawn), which campaigned on an anti-immigration ticket, captured 7% of the vote – enough to place 19 deputies in the 300-seat house for the first time since the collapse of military rule in 1974. Syriza, a coalition of radical left and green groups, took 16.6% of the vote – the second largest share.

What are the social and political implications of the vote? It's tempting to read such a flight to the extremes as a classic rejection of incumbency. Meaning the vote doesn't affirm anything about the electorate, apart from widespread dissatisfaction.

Voters went out of their way to "punish" mainstream parties widely blamed for years of fiscal mismanagement. "How can we vote for parties to be part of the solution when they got us in this mess in the first place?" asked Poppi Stathera, a mother of two, who said she had been out of work for the past year. "We've been completely destroyed. Our country is in ruins."

The Greece election is not to be compared, however, to the usual midterm cleaning of the stables in the US Congress. The fatal riots in Greece of the last two summers raised the specter of societal collapse.

Voters may have been rejecting austerity, but there is also the sense that they were giving voice to a deep sense of insecurity – the kind of feeling that drives support to the political extremes. Paul Krugman sees parallels with the pre-WWII era:

And since all the respectable people are inside the political tent, backing and being identified with failed policies, that means a big vote for extremists right and left.

And yes, the echoes of the 1930s are very strong.

1.08pm ET/6.08pm BST: As an addendum to our last post, we want to direct you to Maria Margaronis' illuminating column today, "Greece takes a leap into the dark, driven by defiance and despair." Margaronis traces the old lines of division submerged beneath the weekend tallies:

As elsewhere in Europe, the draining away of the centre has revealed a jagged landscape: the shorthand of "extremes of left and right" doesn't begin to map it. The most obvious rift in Greece in the last months – a rift that's been described to me more than once as a "civil war"– has been between those who are for and against the "memorandum", the EU/IMF schedule of demands. The pro-memorandum forces want to keep Greece in the eurozone at any cost; most of their opponents also want to stay in Europe – but not of "Merkozy", austerity and the banks.

Across that rift runs an older, deeper one, whose roots go back at least as far as to the actual civil war that followed the Axis occupation, leading to 30 years in which the left was outlawed, and culminating in the neo-fascist junta of 1967 to 1974. The social and political collapse brought by the crisis has revived those memories, too, as well as old family loyalties. In the summer of 2011, when the aganaktismenoi ("outraged") of Syntagma Square briefly became the darlings of the foreign media, conservative truck drivers could rub shoulders with eco warriors and direct democracy mavens; the Greek flag could stand for self-determination as well as nationalism. But not any more.

1.20pm ET/6.20pm BST:What did François Hollande promise the French to win their votes? The Economist presents a summary under the headline, "Here comes the hard part":

Most of his campaign pledges—such as a boost in welfare benefits at the start of the school year, an extra 60,000 teaching jobs, and a partial reversal of the retirement age from 62 to 60 years—involve extra spending. Yet in France public spending already accounts for 56% of GDP, and the overall tax take is also high. And the IMF is forecasting a deficit closer to 3.9% for 2013. Mr Hollande will have very little room to manoeuvre. Winning the election was one thing; the hard part is about to begin.

1.35pm ET/6.35pm BST: Turning now to Spain, where a shake-up in the banking industry overlaps with the political shake-ups elsewhere on the continent.

With the election of Hollande, Spain may see some relief in its pursuit of tight budgetary targets imposed by agreement last year. Now the conservative prime minister has indicated that one beneficiary of any new budgetary breathing room would likely be the banking sector.

Here's the Guardian's Giles Tremlett in Madrid:

Denis Doyle

One of Spain's most high-profile financiers, Rodrigo Rato, resigned Monday ashead of the country's third-largest bank, Bankia, just hours after prime minister Mariano Rajoy announced a major shake-up of the troubled banking sector.

Rato's surprise departure was seen as proof that ailing Bankia, which holds 10% of the country's deposits, was about to be rescued by the Spanish government.

Bankia now looks likely be the centrepiece of a fresh round of financial sector reforms as Rajoy tries to boost confidence in a country that lies at the heart of the eurozone crisis.

Rajoy looked ready to backtrack on pledges not to use more public money on banks. "The last thing I would do would be to inject or lend public money but if it is necessary I would not hesitate to do it, just as other European countries have done," Rajoy told a radio interviewer yesterday.

He was speaking as the financial markets attempted to digest the implications of the election of the Socialist François Hollande as president in France and the outcome of the Greek elections where the formation of a government looked unlikely.

Rajoy said details of the shake-up in Spain would come after Friday's cabinet meeting, but there were rumours that a Bankia announcement would come sooner.

"The objective is to send a strong signal to the markets and also to the International Monetary Fund and other international partners that the (Bankia) plan is ambitious and strong and will complete our ongoing banking reform," an official source told Reuters.

1.43pm ET/6.43pm BST:Which is more significant: the election of Hollande or the political upheaval in Greece?

Britain's former foreign secretary sounds as if he might be persuaded to entertain the idea that François Hollande is not the best thing that's ever happened to Europe. But he's much more concerned about developments further south:

In Paris the CAC 40 index ended the day up 1.65%, while in Frankfurt the DAX 30 finished 0.12% up – nothing to shout about but a clear indication that as far as investors are concerned, the political turmoil is a side show.

In London the markets were closed for a public holiday.

1.52pm ET/6.52pm BST: Warren Buffett thinks the euro was a mistake – at least as it was carried out.

That's what the billionaire investor, who is giving frequent interviews for the annual meeting of his company, Berkshire Hathaway, just told Fox Business.

"The problems facing Europe transcend those in any specific country. They have to work out the rules under which 17 countries can work together," Buffett told Fox.

"I think maybe it was a mistake; it was a mistake as it was done. Now the question is whether you can modify the original concept in some way to make this more workable than it is proving to be. Getting out of it would be an enormous problem."

Buffett was asked if the euro was a mistake.

"I think that getting out of it would be an enormous mistake too," he replied. "I think maybe it was a mistake as it was done. In fact I can say it was a mistake as it was done. Now the question is can you modify the original concept in some way that makes this more workable than it's proving to be."

2.02pm ET/7.02pm BST: The top vote-getter in Sunday's elections in Greece has announced that efforts to form a coalition government have failed.

Antonis Samaras' conservative New Democracy party garnered 18.9% of the vote. But the party cannot draw together sufficient allies to govern, the Guardian's Helena Smith reports.

"We did whatever was possible" Samaras told Greeks in a national address Monday night. He said he had reached out to every party with the exception of the extreme right Chrysi Avgi.

"I have informed the president [of the failed effots] and returned the mandate," Samaras said.

Now the Radical Left Coalition party, which came in second, will get a chance to put together a ruling alliance. RLC head Alexis Tsipras will have three days to seek a coalition.

If his talks fail, according to the Associated Press, the party that came in third in Sunday's vote will get the mandate. No agreement could force new elections next month.

2.38pm ET/7.38pm BST: How will the German authors of Europe's austerity program greet the Hollande presidency? Will they be biding their time until they can say "I told you so"? Would London like to see Hollande fail, out of spite?

It's not clear to me that the EU can remain fiscally sound while remaining democratic - unless some glimmer of growth returns to somewhere other than Germany. Cameron and Merkel would provide a natural pro-austerity axis, if Britain had actually signed the fiscal pact. What I expect from London is pure anti-French schadenfreude.

Sullivan finds evidence of skepticism in a Telegraph report:

A senior Conservative source told The Daily Telegraph that fears France was about to reverse course would cause turmoil and uncertainty: "Clearly it's going to focus a lot of market attention on the French public finances, which are nothing to write home about. I don't think it is going to make life in the bond markets any easier next week. We haven't chosen austerity because it's fun. We have to do austerity, and so does France. He will have to be very careful about his public spending commitments and the lack of welfare reform."

Hollande realizes that the policy options open to any one nation in a highly integrated European economic area are marginal. From day one of Hollande's campaign, he has focused on Europe. Speaking at the Global Progress summit organized by the Center for American Progress in Madrid last October, two days after becoming the party's nominee, he called for an end to austerity. ...

Like President Obama four years ago, the expectations now resting on Hollande's shoulders are unrealistically high and extend well beyond his national borders. And like in 2008 change today will take time. But by focusing on progressive, pragmatic, pro-growth policies, the new French president has set out a realistic and achievable vision of the Europe we need.

3.46pm ET/8.46pm BST:More in from Athens where Helena Smith says the Left Coalition (Syriza) is vowing to make "good use" of the three days it will have at its disposal to try to form a "durable" government.

Antonis Samaras of the conservative New Democracy party, the first-place election winner, announced earlier this afternoon that it had failed to put together a governing coalition.

"We are the second biggest party. We are very aware of our responsibility towards the Greek people and will make good use of our mandate," Dimitris Stratoulis, a party official, has just told Mega TV.

At no other time in the nation's modern history have radical leftists received a mandate to form a government.

"Our aim is form a government of the left that will liberate the country from the shameful loan agreement it has signed up to," said Stratoulis, rebuffing suggestions that the party was bent on elections being repeated so that it could improve its poll ratings further.

WH: "President Obama said he & Mrs. Obama extend their very best wishes to President Sarkozy & his wife Carla in their future endeavors"

4.07pm ET/9.07pm BST:"Stocks Shrug Off Europe" – that's the CNBC headline at the close of trading on the East coast. The Dow Jones index closed down 0.2%, Nasdaq closed up 1.42% and the S&P 500 closed up .54%.

Anyone searching for an explanation of why the markets didn't "react" to the change of government in France and lack of a government in Greece might do well to consider how "easy" it would have been to explain a wild market reaction to the likely crumbling of the eurozone.

The standard explanation is to say that the information was pre-baked in the market cake, and that traders anticipated the results.

We wonder if the traders can tell us what's going to happen next. Because we sure would like to know.

5.06pm ET/10.06pm BST: Here's a less prosaic take on the French elections.

5.45pm ET/10.45pm BST: We're going to wrap up our live blog coverage of how the European election results are playing around the world. Here's a summary of the latest developments:

•The top Greek vote-getter, the conservative New Democracy party, announced that it had failed to form a viable governing coalition. The challenge of forming a government now passes to the far-left Syriza party, which won the second most votes Sunday. If they fail, third place gets a crack.

•US markets didn't move much on Monday, despite the excitement overseas. The euro closed slightly up after a steep dropoff in overnight trading.

•If François Hollande wants growth for France, he's going to have to cut a deal that touches all of Europe, analysts agree. Hollande will begin by trying to relax austerity measures written in Germany and applied everywhere from Spain to Greece. He is preparing to take power a week from tomorrow, May 15.